Respuesta :
Answer:
3x=2-3y
y=-x-3
Step-by-step explanation:
Find the slope of the original line and use the point-slope formula
to find the line parallel to
The equation of line that is parallel to 3x = 2 - 2y and passes through (3, -6) is y = -x - 3
Solution:
Given, line equation is 3x = 2 – 3y
⇒ 3x + 3y = 2 ⇒ (1)
The point is (3, -6)
We have to find the equation of a line which is parallel to given line and passes through given point.
Now, let us find the slope of the given equation
[tex]\text { slope }=\frac{-\mathrm{x} \text { coefficient }}{\mathrm{y} \text { coefficient }}=\frac{-3}{3}=-1[/tex]
So, slope of line is -1
We also know that, slopes of parallel lines are equal, then slope of our required line is – 1.
Then, let us find our line equation using point slope form
[tex]\mathrm{y}-\mathrm{y}_{1}=\mathrm{m}\left(\mathrm{x}-\mathrm{x}_{1}\right)[/tex]
Where "m" is the slope of the line
[tex]\text { Here in our problem, } m=-1,\left(x_{1}, y_{1}\right)=(3,-6)[/tex]
By substituting the values in point slope form we get,
[tex]\begin{array}{l}{\rightarrow y-(-6)=-1(x-3)} \\\\ {\rightarrow y+6=-1(x-3)} \\\\ {\rightarrow y=-x-3}\end{array}[/tex]
Hence the required equation is y = -x - 3
